Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 18, 08 December 2023
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Relativistic path integrals
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Abstract
Classical and Quantum mechanics are the two milestones of physics and mathematics. The path integral describes the generalised form of action from classical to quantum mechanics. This paper has reviewed some fundamental concepts and results in classical dynamics and quantum mechanics. The research method of the whole project is mainly theoretical derivations of applied mathematics and mathematical physics. This paper provides different perspectives to investigate the applications of path integrals. This paper also builds a connection between path integrals and the Unruh temperature.
Keywords
path integrals, simple harmonic, oscillator, relativistic quantum, mechanics, unruh effect, detector models
References
1. Feynman RP, Hibbs AR. Quantum Mechanics and Path Integrals. New York: Dover Publications; 2010 .
2. Bailin D, Love A. Introduction to Gauge Field Theory. Bristol: Institute of Physics; 1993.
3. Schulman LS. Techniques and Applications of Path Integration. New York: Dover Publications; 2005 .
4. Ballentine LE. Quantum Mechanics : a Modern Development. New Jersey: World Scientific; 2015.
5. Goldstein H. Classical Mechanics. San Francisco: Addison Wesley; 2002.
6. Perepelitsa DV. Path Integrals in Quantum Mechanics.
7. Feymann RP, Vernon FL. The Theory of a General Quantum System Interacting with a Linear Dissipative System. Annals of Physics. 1963;24:118-73.
8. Landau LD, Lifshitz EM. The Classical Theory of Fields. Amsterdam: ButterworthHeinemann; 2008.
9. Cushman-Roisin B, Beckers JM. Introduction to Geophysical Fluid Dynamics Physical and Numerical Aspects. Massachusetts: Academic Press; 2011.
10. Dirac PAM. The Quantum Theory of the Electron. Proceedings of the Royal Society of London Series A, Containing Papers of a Mathematical and Physical Character. 1928;117(778):610-24.
11. Matsas G. The Fulling-Davies-Unruh Effect is Mandatory: The Proton's Testimony. International Journal of Modern Physics. 2002;11(10):1573-1577.
12. Unruh WG. Notes on black-hole evaporation. Phys Rev. 1976;14(870).
13. Hawking SW. Black Hole Explosions? Nature. 1974;248(30-31).
14. Hawking SW, Israel W, Einstein A. General Relativity : an Einstein Centenary Survey. Cambridge: Cambridge University Press; 1979.
15. Anglin JR. Influence Functionals and the Accelerating Detector. PhysRev. 1992;D47:4525-37.
16. Das A. Topics in Finite Temperature Field Theory. arXiv preprint hep-ph/0004125. 2000.
17. Buchdahl HA. General Relativistic Fluid Spheres. Phys Rev. 1959;116(1027).
Data Availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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- Volume Title
- Proceedings of the 2nd International Conference on Computing Innovation and Applied Physics
- ISBN (Print)
- 978-1-83558-201-5
- ISBN (Online)
- 978-1-83558-202-2
- Published Date
- 08 December 2023
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/18/20230292
- Copyright
- 08 December 2023
- Open Access
- This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited